I have the fewest skin issues when I eat low-carb, especially no wheat and low-grain. When I eat high-carb I have rosacea, mild cystic acne, seborrheic dermatitis, swollen inflamed skin and other rashes.
This of course makes me wonder whether it's a very individual thing. Another possibility is the source of my protein. I do eat some red meat such as beef, pork, and bison, but red meat isn't the only or primary source of my protein. I eat eggs, chicken (mostly dark meat because it's cheapest),turkey, all sorts of fresh, frozen, and canned fish and seafood, tvp (soy protein), fermented and aged dairy (yogurt, greek yogurt, sour cream, and cheeses both soft and hard), pumpkin and sunflower seeds, nuts, some whey protein (in smoothies)...
I have read that chicken (even factory raised chicken) isn't generally raised with hormones (antibiotics yes, but hormones, no). I don't know for certain this is true, but if it's the hormones in red meat that can trigger skin breakouts, this would make sense.
I've also read that the hormones in beef also end up in dairy, but while I eat dairy, it's also not my main protein. Chicken and fish are my main animal proteins. Soy also has plant estrogens, but again while I eat soy I don't eat it daily or even weekly.
It's also possible that you have an actual allergy or sensitivity. For me, wheat is my biggest breakout trigger. When I eat wheat, especially in a wheat/yeast combo like bread, I will break out with some type of inflammation or rash on my face. Either on the chin (the skin will be red or pink, and I'll have a lot of very tiny pimples), or a "butterfly" rash across the cheeks and nose, or my cheeks, nose and chin will actually redden and swell (so that the pores are very huge and the skin looks like the skin of an orange and the color will range from light pink to almost magenta). Sometimes I'll break out in large cyst like pimples across my forehead, or I'll get a weird flaking eyebrow "dandruff" (I'm told this is the seborrheic dermatitis).
When I went to a dermatologist, she recommended using Head and Shoulders type shampoos (with zinc pyrithione listed as an ingredient - I use generic brands) as my only shampoo and soap. I use it on my body, face, and hair (and usually use the one with the built in conditioner because the shampoo alone tends to be drying).
Between eating low-carb and using the Head and Shoulders, my skin hasn't been this clear since before puberty.
To find out which food(s) are causing your skin issues, I'd suggest a food journal and an elimination diet. If you suspect red meat, then continue to eat low-carb but avoid red meat and see if the skin issues improve. If it's not the red-meat, it might be another high-protein food. You might want to see an allergy specialist to rule out allergies.
I'd recommend the Head and Shoulders regardless, because it's been such a godsend for me that I recommend it to everyone.